Optimization Methods for Designing Sequences with Low Autocorrelation Sidelobes

Abstract: Unimodular sequences with low autocorrelations are desired in many applications, especially in the area of radar and code-division multiple access (CDMA). In this paper, we propose a new algorithm to design unimodular sequences with low integrated sidelobe level (ISL), which is a widely used measure of the goodness of a sequence's correlation property. The algorithm falls into the general framework of majorization-minimization (MM) algorithms and thus shares the monotonic property of such algorithms. In addition, the algorithm can be implemented via fast Fourier transform (FFT) operations and thus is computationally efficient. Furthermore, after some modifications the algorithm can be adapted to incorporate spectral constraints, which makes the design more flexible. Numerical experiments show that the proposed algorithms outperform existing algorithms in terms of both the quality of designed sequences and the computational complexity.

• The paper introduces the MISL algorithm which uses majorization-minimization (MM) to directly minimize Integrated Sidelobe Level (ISL) for both aperiodic and periodic autocorrelation.
• The MISL algorithm achieves lower ISL and is more computationally efficient for long sequences compared to CAN, maintaining monotonic convergence.
• Implemented via FFT, MISL is scalable for long sequences and allows integration of spectral constraints, making it practical for advanced radar and communication systems.

Optimization Methods for Designing Sequences with Low Autocorrelation Sidelobes

This paper presents a novel algorithm for the design of unimodular sequences featuring low integrated sidelobe levels (ISL), which are crucial in applications such as radar and code-division multiple access (CDMA) systems. The primary contribution of the research is a Monotonic minimizer for Integrated Sidelobe Level (MISL) algorithm, which directly minimizes the ISL metric—both aperiodic and periodic autocorrelation—through a dual application of majorization-minimization (MM) methodology.

Summary of Contributions

The authors address a long-standing challenge in digital communications, namely the design of sequences with minimal autocorrelation sidelobes, which enhances the performance of radar systems in detecting weak signals and fortifies synchronization in CDMA systems. Their approach is distinguished by:

1. Algorithm Design: The MISL leverages the properties of MM methods, maintaining their monotonic convergence, and enables efficient computation using Fast Fourier Transform (FFT).
2. Numerical Efficiency: Unlike previous methods—such as the CAN (Cyclic Algorithm New)—MISL offers both computational efficiency and robustness for longer sequences, suggesting its potential in handling complex system requirements.
3. Spectral Flexibility: The algorithm is versatile in that it allows the integration of spectral constraints without compromising performance, thereby accommodating practical scenarios where spectral limits are enforced.

Key Results

Comparing to existing methodologies, the MISL algorithm shows superior performance not just in terms of computation time but also in achieving lower ISL values which translate to a better quality of the designed sequences. The numerical experimentation reveals that CAN, while effective, does not maintain the monotonic convergence of MISL and may settle into suboptimal solutions, particularly when initialized differently.

The expedited MISL variations, including acceleration via fixed point theory and backtracking schemes, further enhance the convergence speed, making the algorithm applicable to real-time systems needing rapid computation.

Implications and Future Prospects

The proposed MISL algorithm significantly impacts the design landscape for sequences with low ISL. From a practical perspective, its implementation via FFT makes it scalable for long sequences, enabling its potential application in newer communication paradigms where rapid computation is vital. The development of spectral-MISL to handle additional constraints aligns well with demands in cognitive radio and other advanced radar systems that operate in dynamically defined spectral environments.

Theoretically, using majorization strategies to progressively refine MM applications can yield deeper insights into optimization-related computational practices. Future developments may explore adaptive MISL extensions, which can dynamically adjust majorization criteria based on real-time performance metrics.

In summary, the research provides a methodologically sound and computationally viable pathway toward optimizing sequence design under various practical constraints, enlarging the toolset available to engineers and researchers in the communications domain.